Vol. 67, No. 2, 1976

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ISSN: 0030-8730
Principal and induced fibrations

Cheong Seng Hoo

Vol. 67 (1976), No. 2, 389–400
Abstract

In this paper, the following is proved.

Theorem. Let F→iE→pB be a fibration in which E and B have the homotopy type of CW complexes. Suppose that F is (n 1) connected and B is (m 1) connected, where m,n 2. Let l = min(m,n), k = min(2m 1,2n). Suppose that there exists a map E ×F E of type (1,i). If πq(B) = 0 for all q n + l, then the fibration is Ganea principal. If further πq(F) = 0 for all q n + k, then the fibration is induced by some map f : B Y for some space Y. The dual is also true.

Mathematical Subject Classification
Primary: 55F05, 55F05
Milestones
Received: 6 December 1975
Published: 1 December 1976
Authors
Cheong Seng Hoo